The shielding constant for the last electron in Sc is ______.

Answer

To find the shielding constant for the last electron in Scandium (Sc), we will follow these steps:

### Step 1: Identify the Atomic Number and Electronic Configuration
- The atomic number of Scandium (Sc) is 21.
- The electronic configuration of Sc is:
\[ 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 3d^1 \, 4s^2 \]

### Step 2: Determine the Last Electron
- The last electron in Sc is in the 4s orbital.

### Step 3: Identify the Principal Quantum Numbers
- The principal quantum number (n) for the last electron (4s) is \( n = 4 \).
- The electrons in the previous shells are:
- \( n - 1 = 3 \) (which includes 3s, 3p, and 3d)
- \( n - 2 = 2 \) (which includes 2s and 2p)

### Step 4: Calculate the Shielding Constant
- The shielding constant (σ) can be calculated using the formula:
\[ \sigma = 0.35 \times (number \, of \, electrons \, in \, n) + 0.85 \times (number \, of \, electrons \, in \, n-1) + 1.00 \times (number \, of \, electrons \, in \, n-2) \]

### Step 5: Substitute the Values
- For the last electron in Sc (4s):
- Number of electrons in \( n = 4 \): 2 (from 4s)
- Number of electrons in \( n - 1 = 3 \): 8 (from 3s, 3p, and 3d)
- Number of electrons in \( n - 2 = 2 \): 10 (from 2s and 2p)

Using the formula:
\[ \sigma = 0.35 \times 2 + 0.85 \times 8 + 1.00 \times 10 \]

### Step 6: Perform the Calculations
- Calculate each term:
- \( 0.35 \times 2 = 0.70 \)
- \( 0.85 \times 8 = 6.80 \)
- \( 1.00 \times 10 = 10.00 \)

Now, sum these values:
\[ \sigma = 0.70 + 6.80 + 10.00 = 17.50 \]

### Step 7: Round to the Nearest Whole Number
- The shielding constant is typically rounded to the nearest whole number, so:
\[ \sigma \approx 18 \]

### Final Answer
The shielding constant for the last electron in Scandium is **18**.

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